Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #22608525 | C2 | semidirect |
| 5. #22608442 | C2 | semidirect |
| 6. #22607802 | C2 | semidirect |
| 7. C73×#1300 | C2 | semidirect |
| 11. #17988883 | C4 | semidirect |
| 12. #17988878 | C4 | semidirect |
| 13. #17988798 | C4 | semidirect |
| 14. #17988793 | C4 | semidirect |
| 200. #1300 | D73 | semidirect |
| 202. C73 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620094 | 2 |
| #22618949 | 2 |
| #22609742 | 2 |
| #22608525 | 2 |
| #22608442 | 2 |
| #22607802 | 2 |
| C73×#1300 | 2 |
| #9160 | 73 |